R Notebook
library(tidyverse)Registered S3 methods overwritten by 'dbplyr':
method from
print.tbl_lazy
print.tbl_sql
── Attaching packages ──────────────────────────────────────── tidyverse 1.3.1 ──
✔ ggplot2 3.3.6 ✔ purrr 0.3.4
✔ tibble 3.1.7 ✔ dplyr 1.0.9
✔ tidyr 1.2.0 ✔ stringr 1.4.0
✔ readr 2.1.2 ✔ forcats 0.5.1
── Conflicts ─────────────────────────────────────────── tidyverse_conflicts() ──
✖ dplyr::filter() masks stats::filter()
✖ dplyr::lag() masks stats::lag()library(modelr)
library(skimr)
library(GGally)Registered S3 method overwritten by 'GGally':
method from
+.gg ggplot2###cleaning for regression
kc_houses <- read_csv("data/kc_house_data.csv")Rows: 21613 Columns: 21
── Column specification ─────────────────────────────────────────────────────────
Delimiter: ","
chr (1): id
dbl (19): price, bedrooms, bathrooms, sqft_living, sqft_lot, floors, waterfr...
dttm (1): date
ℹ Use `spec()` to retrieve the full column specification for this data.
ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.###removing aliases
alias(lm(price ~ ., data = kc_houses))
Model :
price ~ bedrooms + bathrooms + sqft_living + sqft_lot + floors +
waterfront + view + condition + grade + yr_built + yr_renovated +
lat + long + sqft_living15 + sqft_lot15###choosing first predictor for model
ggpairs(kc_houses_numeric)
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ggsave("nonnumeric.png")Saving 6.22 x 3.84 in image
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waterfront, view and grade have potential sqft_living, sqft_living15, bathrooms, bedrooms, lat
model1a <- lm(price ~ sqft_living,
data = kc_houses)
autoplot(model1a)
summary(model1a) #violates normal distribution and scale location
Call:
lm(formula = price ~ sqft_living, data = kc_houses)
Residuals:
Min 1Q Median 3Q Max
-1476062 -147486 -24043 106182 4362067
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -43580.743 4402.690 -9.899 <2e-16 ***
sqft_living 280.624 1.936 144.920 <2e-16 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 261500 on 21611 degrees of freedom
Multiple R-squared: 0.4929, Adjusted R-squared: 0.4928
F-statistic: 2.1e+04 on 1 and 21611 DF, p-value: < 2.2e-16kc_houses <- kc_houses %>%
mutate(ln_sqft_living = log(sqft_living))
model1b <- lm(price ~ ln_sqft_living,
data = kc_houses)
autoplot(model1b)
summary(model1b)
Call:
lm(formula = price ~ ln_sqft_living, data = kc_houses)
Residuals:
Min 1Q Median 3Q Max
-606252 -170067 -33139 106342 6183772
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -3451377 35169 -98.14 <2e-16 ***
ln_sqft_living 528648 4651 113.67 <2e-16 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 290400 on 21611 degrees of freedom
Multiple R-squared: 0.3742, Adjusted R-squared: 0.3742
F-statistic: 1.292e+04 on 1 and 21611 DF, p-value: < 2.2e-16reject sqft_living and ln_sqft_living based on diagnostic plots
model1c <- lm(price ~ sqft_living15,
data = kc_houses)
autoplot(model1c)
summary(model1c)
Call:
lm(formula = price ~ sqft_living15, data = kc_houses)
Residuals:
Min 1Q Median 3Q Max
-842924 -162153 -43709 95431 6547397
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -82807.195 6208.029 -13.34 <2e-16 ***
sqft_living15 313.556 2.954 106.14 <2e-16 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 297700 on 21611 degrees of freedom
Multiple R-squared: 0.3427, Adjusted R-squared: 0.3426
F-statistic: 1.127e+04 on 1 and 21611 DF, p-value: < 2.2e-16kc_houses <- kc_houses %>%
mutate(ln_sqft_living15 = log(sqft_living15))
model1d <- lm(price ~ ln_sqft_living15,
data = kc_houses)
autoplot(model1d)
summary(model1d)
Call:
lm(formula = price ~ ln_sqft_living15, data = kc_houses)
Residuals:
Min 1Q Median 3Q Max
-751080 -173399 -43738 98941 6708980
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -4057333 48284 -84.03 <2e-16 ***
ln_sqft_living15 609783 6398 95.31 <2e-16 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 308100 on 21611 degrees of freedom
Multiple R-squared: 0.2959, Adjusted R-squared: 0.2959
F-statistic: 9083 on 1 and 21611 DF, p-value: < 2.2e-16model1e <- lm(price ~ bathrooms,
data = kc_houses)
autoplot(model1e)
summary(model1e)
Call:
lm(formula = price ~ bathrooms, data = kc_houses)
Residuals:
Min 1Q Median 3Q Max
-1438157 -184525 -41525 113220 5925322
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 10708 6211 1.724 0.0847 .
bathrooms 250326 2760 90.714 <2e-16 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 312400 on 21611 degrees of freedom
Multiple R-squared: 0.2758, Adjusted R-squared: 0.2757
F-statistic: 8229 on 1 and 21611 DF, p-value: < 2.2e-16
kc_houses <- kc_houses %>%
mutate(ln_bathrooms = log(1 + bathrooms))
model1f <- lm(price ~ ln_bathrooms,
data = kc_houses)
autoplot(model1f)
summary(model1f)
Call:
lm(formula = price ~ ln_bathrooms, data = kc_houses)
Residuals:
Min 1Q Median 3Q Max
-809328 -193575 -44701 109343 6400950
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -227900 9874 -23.08 <2e-16 ***
ln_bathrooms 694945 8711 79.78 <2e-16 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 322700 on 21611 degrees of freedom
Multiple R-squared: 0.2275, Adjusted R-squared: 0.2275
F-statistic: 6365 on 1 and 21611 DF, p-value: < 2.2e-16waterfront, view and grade have potential
model1g <- lm(price ~ grade,
data = kc_houses)
autoplot(model1g)Warning: Removed 2313 row(s) containing missing values (geom_path).
Warning: Removed 1 rows containing missing values (geom_point).
Warning: Removed 1 row(s) containing missing values (geom_path).
summary(model1g)
Call:
lm(formula = price ~ grade, data = kc_houses)
Residuals:
Min 1Q Median 3Q Max
-1929615 -135853 -35090 89080 5565658
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 142000 254499 0.558 0.576878
grade3 63667 293870 0.217 0.828484
grade4 72381 258849 0.280 0.779767
grade5 106524 255024 0.418 0.676169
grade6 159920 254561 0.628 0.529868
grade7 260590 254513 1.024 0.305904
grade8 400853 254520 1.575 0.115285
grade9 631513 254547 2.481 0.013112 *
grade10 929771 254611 3.652 0.000261 ***
grade11 1354842 254817 5.317 1.07e-07 ***
grade12 2049222 255909 8.008 1.23e-15 ***
grade13 3567615 264106 13.508 < 2e-16 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 254500 on 21601 degrees of freedom
Multiple R-squared: 0.5197, Adjusted R-squared: 0.5195
F-statistic: 2125 on 11 and 21601 DF, p-value: < 2.2e-16model1h <- lm(price ~ view,
data = kc_houses)
autoplot(model1h)
summary(model1h)
Call:
lm(formula = price ~ view, data = kc_houses)
Residuals:
Min 1Q Median 3Q Max
-1211711 -196564 -67564 108436 6728035
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 496564 2399 207.02 <2e-16 ***
view1 315717 18533 17.04 <2e-16 ***
view2 295837 11054 26.76 <2e-16 ***
view3 475401 15020 31.65 <2e-16 ***
view4 967147 18901 51.17 <2e-16 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 334900 on 21608 degrees of freedom
Multiple R-squared: 0.1682, Adjusted R-squared: 0.1681
F-statistic: 1093 on 4 and 21608 DF, p-value: < 2.2e-16model1b has the highest r^2 and the least horiffic diagnostic plots
###second predicotr to explain residuals
price_resid <- kc_houses %>%
add_residuals(model1b) %>%
select(-c(price, grade))
price_resid %>%
ggpairs()
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plot: [17,4] [=========================================>-----] 90% est: 5s
plot: [17,5] [==========================================>----] 90% est: 4s
plot: [17,6] [==========================================>----] 91% est: 4s `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
plot: [17,7] [==========================================>----] 91% est: 4s `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
plot: [17,8] [==========================================>----] 91% est: 4s `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
plot: [17,9] [==========================================>----] 92% est: 4s
plot: [17,10] [=========================================>----] 92% est: 4s `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
plot: [17,11] [=========================================>----] 92% est: 4s
plot: [17,12] [==========================================>---] 93% est: 3s
plot: [17,13] [==========================================>---] 93% est: 3s
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plot: [18,4] [============================================>--] 96% est: 2s
plot: [18,5] [============================================>--] 96% est: 2s
plot: [18,6] [============================================>--] 96% est: 2s `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
plot: [18,7] [============================================>--] 97% est: 2s `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
plot: [18,8] [=============================================>-] 97% est: 1s `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
plot: [18,9] [=============================================>-] 97% est: 1s
plot: [18,10] [============================================>-] 98% est: 1s `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
plot: [18,11] [============================================>-] 98% est: 1s
plot: [18,12] [============================================>-] 98% est: 1s
plot: [18,13] [============================================>-] 98% est: 1s
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plot: [18,15] [=============================================>] 99% est: 0s
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plot: [18,17] [=============================================>]100% est: 0s
plot: [18,18] [==============================================]100% est: 0s
ggsave("resid.png", height = 20, width = 20)
plot: [1,1] [------------------------------------------------] 0% est: 0s
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plot: [5,15] [============>----------------------------------] 27% est:21s
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plot: [5,17] [============>----------------------------------] 27% est:21s
plot: [5,18] [============>----------------------------------] 28% est:21s
plot: [6,1] [============>-----------------------------------] 28% est:21s `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
plot: [6,2] [=============>----------------------------------] 28% est:21s `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
plot: [6,3] [=============>----------------------------------] 29% est:21s `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
plot: [6,4] [=============>----------------------------------] 29% est:22s `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
plot: [6,5] [=============>----------------------------------] 29% est:22s `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
plot: [6,6] [=============>----------------------------------] 30% est:22s
plot: [6,7] [=============>----------------------------------] 30% est:22s
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plot: [6,15] [==============>--------------------------------] 32% est:21s
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plot: [6,17] [===============>-------------------------------] 33% est:21s
plot: [6,18] [===============>-------------------------------] 33% est:21s
plot: [7,1] [===============>--------------------------------] 34% est:21s `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
plot: [7,2] [===============>--------------------------------] 34% est:22s `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
plot: [7,3] [===============>--------------------------------] 34% est:22s `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
plot: [7,4] [================>-------------------------------] 35% est:23s `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
plot: [7,5] [================>-------------------------------] 35% est:23s `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
plot: [7,6] [================>-------------------------------] 35% est:24s
plot: [7,7] [================>-------------------------------] 35% est:24s
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plot: [7,15] [=================>-----------------------------] 38% est:23s
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plot: [7,17] [=================>-----------------------------] 39% est:23s
plot: [7,18] [=================>-----------------------------] 39% est:23s
plot: [8,1] [==================>-----------------------------] 39% est:23s `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
plot: [8,2] [==================>-----------------------------] 40% est:23s `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
plot: [8,3] [==================>-----------------------------] 40% est:24s `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
plot: [8,4] [==================>-----------------------------] 40% est:24s `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
plot: [8,5] [==================>-----------------------------] 40% est:24s `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
plot: [8,6] [===================>----------------------------] 41% est:25s
plot: [8,7] [===================>----------------------------] 41% est:25s
plot: [8,8] [===================>----------------------------] 41% est:25s
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plot: [9,2] [=====================>--------------------------] 45% est:24s
plot: [9,3] [=====================>--------------------------] 45% est:23s
plot: [9,4] [=====================>--------------------------] 46% est:23s
plot: [9,5] [=====================>--------------------------] 46% est:23s
plot: [9,6] [=====================>--------------------------] 46% est:23s `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
plot: [9,7] [=====================>--------------------------] 47% est:23s `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
plot: [9,8] [======================>-------------------------] 47% est:23s `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
plot: [9,9] [======================>-------------------------] 47% est:23s
plot: [9,10] [=====================>-------------------------] 48% est:23s
plot: [9,11] [=====================>-------------------------] 48% est:23s
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plot: [9,17] [======================>------------------------] 50% est:22s
plot: [9,18] [=======================>-----------------------] 50% est:22s
plot: [10,1] [=======================>-----------------------] 50% est:22s `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
plot: [10,2] [=======================>-----------------------] 51% est:21s `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
plot: [10,3] [=======================>-----------------------] 51% est:21s `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
plot: [10,4] [=======================>-----------------------] 51% est:21s `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
plot: [10,5] [=======================>-----------------------] 52% est:21s `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
plot: [10,6] [=======================>-----------------------] 52% est:21s
plot: [10,7] [========================>----------------------] 52% est:21s
plot: [10,8] [========================>----------------------] 52% est:21s
plot: [10,9] [========================>----------------------] 53% est:21s `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
plot: [10,10] [=======================>----------------------] 53% est:21s
plot: [10,11] [========================>---------------------] 53% est:21s
plot: [10,12] [========================>---------------------] 54% est:21s
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plot: [11,1] [=========================>---------------------] 56% est:20s
plot: [11,2] [=========================>---------------------] 56% est:19s
plot: [11,3] [==========================>--------------------] 56% est:19s
plot: [11,4] [==========================>--------------------] 57% est:19s
plot: [11,5] [==========================>--------------------] 57% est:19s
plot: [11,6] [==========================>--------------------] 57% est:19s `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
plot: [11,7] [==========================>--------------------] 58% est:19s `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
plot: [11,8] [==========================>--------------------] 58% est:19s `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
plot: [11,9] [==========================>--------------------] 58% est:19s
plot: [11,10] [==========================>-------------------] 59% est:19s `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
plot: [11,11] [==========================>-------------------] 59% est:19s
plot: [11,12] [==========================>-------------------] 59% est:18s
plot: [11,13] [==========================>-------------------] 60% est:18s
plot: [11,14] [===========================>------------------] 60% est:18s
plot: [11,15] [===========================>------------------] 60% est:18s
plot: [11,16] [===========================>------------------] 60% est:18s
plot: [11,17] [===========================>------------------] 61% est:18s
plot: [11,18] [===========================>------------------] 61% est:17s
plot: [12,1] [============================>------------------] 61% est:17s
plot: [12,2] [============================>------------------] 62% est:17s
plot: [12,3] [============================>------------------] 62% est:17s
plot: [12,4] [============================>------------------] 62% est:17s
plot: [12,5] [============================>------------------] 63% est:17s
plot: [12,6] [=============================>-----------------] 63% est:16s `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
plot: [12,7] [=============================>-----------------] 63% est:16s `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
plot: [12,8] [=============================>-----------------] 64% est:16s `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
plot: [12,9] [=============================>-----------------] 64% est:16s
plot: [12,10] [=============================>----------------] 64% est:16s `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
plot: [12,11] [=============================>----------------] 65% est:16s
plot: [12,12] [=============================>----------------] 65% est:16s
plot: [12,13] [=============================>----------------] 65% est:16s
plot: [12,14] [=============================>----------------] 65% est:16s
plot: [12,15] [=============================>----------------] 66% est:16s
plot: [12,16] [=============================>----------------] 66% est:15s
plot: [12,17] [==============================>---------------] 66% est:15s
plot: [12,18] [==============================>---------------] 67% est:15s
plot: [13,1] [==============================>----------------] 67% est:15s
plot: [13,2] [===============================>---------------] 67% est:15s
plot: [13,3] [===============================>---------------] 68% est:15s
plot: [13,4] [===============================>---------------] 68% est:14s
plot: [13,5] [===============================>---------------] 68% est:14s
plot: [13,6] [===============================>---------------] 69% est:14s `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
plot: [13,7] [===============================>---------------] 69% est:14s `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
plot: [13,8] [===============================>---------------] 69% est:14s `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
plot: [13,9] [================================>--------------] 69% est:14s
plot: [13,10] [===============================>--------------] 70% est:14s `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
plot: [13,11] [===============================>--------------] 70% est:14s
plot: [13,12] [===============================>--------------] 70% est:14s
plot: [13,13] [================================>-------------] 71% est:13s
plot: [13,14] [================================>-------------] 71% est:13s
plot: [13,15] [================================>-------------] 71% est:13s
plot: [13,16] [================================>-------------] 72% est:13s
plot: [13,17] [================================>-------------] 72% est:13s
plot: [13,18] [================================>-------------] 72% est:13s
plot: [14,1] [=================================>-------------] 73% est:12s
plot: [14,2] [=================================>-------------] 73% est:12s
plot: [14,3] [=================================>-------------] 73% est:12s
plot: [14,4] [==================================>------------] 73% est:12s
plot: [14,5] [==================================>------------] 74% est:12s
plot: [14,6] [==================================>------------] 74% est:12s `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
plot: [14,7] [==================================>------------] 74% est:12s `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
plot: [14,8] [==================================>------------] 75% est:12s `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
plot: [14,9] [==================================>------------] 75% est:12s
plot: [14,10] [==================================>-----------] 75% est:11s `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
plot: [14,11] [==================================>-----------] 76% est:11s
plot: [14,12] [==================================>-----------] 76% est:11s
plot: [14,13] [==================================>-----------] 76% est:11s
plot: [14,14] [==================================>-----------] 77% est:11s
plot: [14,15] [==================================>-----------] 77% est:11s
plot: [14,16] [==================================>-----------] 77% est:10s
plot: [14,17] [===================================>----------] 77% est:10s
plot: [14,18] [===================================>----------] 78% est:10s
plot: [15,1] [====================================>----------] 78% est:10s
plot: [15,2] [====================================>----------] 78% est:10s
plot: [15,3] [====================================>----------] 79% est:10s
plot: [15,4] [====================================>----------] 79% est:10s
plot: [15,5] [====================================>----------] 79% est: 9s
plot: [15,6] [====================================>----------] 80% est: 9s `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
plot: [15,7] [=====================================>---------] 80% est: 9s `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
plot: [15,8] [=====================================>---------] 80% est: 9s `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
plot: [15,9] [=====================================>---------] 81% est: 9s
plot: [15,10] [====================================>---------] 81% est: 9s `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
plot: [15,11] [====================================>---------] 81% est: 9s
plot: [15,12] [====================================>---------] 81% est: 9s
plot: [15,13] [=====================================>--------] 82% est: 8s
plot: [15,14] [=====================================>--------] 82% est: 8s
plot: [15,15] [=====================================>--------] 82% est: 8s
plot: [15,16] [=====================================>--------] 83% est: 8s
plot: [15,17] [=====================================>--------] 83% est: 8s
plot: [15,18] [=====================================>--------] 83% est: 8s
plot: [16,1] [======================================>--------] 84% est: 7s
plot: [16,2] [======================================>--------] 84% est: 7s
plot: [16,3] [=======================================>-------] 84% est: 7s
plot: [16,4] [=======================================>-------] 85% est: 7s
plot: [16,5] [=======================================>-------] 85% est: 7s
plot: [16,6] [=======================================>-------] 85% est: 7s `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
plot: [16,7] [=======================================>-------] 85% est: 7s `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
plot: [16,8] [=======================================>-------] 86% est: 7s `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
plot: [16,9] [=======================================>-------] 86% est: 6s
plot: [16,10] [=======================================>------] 86% est: 6s `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
plot: [16,11] [=======================================>------] 87% est: 6s
plot: [16,12] [=======================================>------] 87% est: 6s
plot: [16,13] [=======================================>------] 87% est: 6s
plot: [16,14] [=======================================>------] 88% est: 6s
plot: [16,15] [=======================================>------] 88% est: 6s
plot: [16,16] [========================================>-----] 88% est: 5s
plot: [16,17] [========================================>-----] 89% est: 5s
plot: [16,18] [========================================>-----] 89% est: 5s
plot: [17,1] [=========================================>-----] 89% est: 5s
plot: [17,2] [=========================================>-----] 90% est: 5s
plot: [17,3] [=========================================>-----] 90% est: 5s
plot: [17,4] [=========================================>-----] 90% est: 5s
plot: [17,5] [==========================================>----] 90% est: 4s
plot: [17,6] [==========================================>----] 91% est: 4s `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
plot: [17,7] [==========================================>----] 91% est: 4s `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
plot: [17,8] [==========================================>----] 91% est: 4s `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
plot: [17,9] [==========================================>----] 92% est: 4s
plot: [17,10] [=========================================>----] 92% est: 4s `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
plot: [17,11] [=========================================>----] 92% est: 4s
plot: [17,12] [==========================================>---] 93% est: 3s
plot: [17,13] [==========================================>---] 93% est: 3s
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latitude
summary(model2a)
Call:
lm(formula = price ~ ln_sqft_living + lat, data = kc_houses)
Residuals:
Min 1Q Median 3Q Max
-666157 -143836 -39236 84919 6149214
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -39084630 633250 -61.72 <2e-16 ***
ln_sqft_living 519005 4346 119.42 <2e-16 ***
lat 750757 13324 56.35 <2e-16 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 271200 on 21610 degrees of freedom
Multiple R-squared: 0.4543, Adjusted R-squared: 0.4543
F-statistic: 8997 on 2 and 21610 DF, p-value: < 2.2e-16model2b <- lm(price ~ ln_sqft_living + grade,
data = kc_houses)
autoplot(model2b)Warning: Removed 5684 row(s) containing missing values (geom_path).
Warning: Removed 1 rows containing missing values (geom_point).
Warning: Removed 1 row(s) containing missing values (geom_path).
summary(model2b)
Call:
lm(formula = price ~ ln_sqft_living + grade, data = kc_houses)
Residuals:
Min 1Q Median 3Q Max
-1831009 -132953 -29074 91804 5350712
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -1292505 246541 -5.243 1.60e-07 ***
ln_sqft_living 253004 5886 42.983 < 2e-16 ***
grade3 -117518 282092 -0.417 0.67698
grade4 -122997 248489 -0.495 0.62062
grade5 -186446 244871 -0.761 0.44642
grade6 -185092 244464 -0.757 0.44898
grade7 -174110 244495 -0.712 0.47640
grade8 -100494 244570 -0.411 0.68115
grade9 58723 244682 0.240 0.81033
grade10 304045 244813 1.242 0.21427
grade11 673027 245092 2.746 0.00604 **
grade12 1314002 246220 5.337 9.56e-08 ***
grade13 2754255 254198 10.835 < 2e-16 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 244300 on 21600 degrees of freedom
Multiple R-squared: 0.5575, Adjusted R-squared: 0.5573
F-statistic: 2268 on 12 and 21600 DF, p-value: < 2.2e-16anova(model1b, model2b)Analysis of Variance Table
Model 1: price ~ ln_sqft_living
Model 2: price ~ ln_sqft_living + grade
Res.Df RSS Df Sum of Sq F Pr(>F)
1 21611 1.8230e+15
2 21600 1.2888e+15 11 5.3411e+14 813.75 < 2.2e-16 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1include all levels in our model due to statistical significance 2b is champ!!
###third predictor
price_resid <- kc_houses %>%
add_residuals(model2b) %>%
select(-c(price, ln_sqft_living, grade))
price_resid %>%
ggpairs()
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ggsave("resid2.png", height = 20, width = 20)
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latitude?
model3a <- lm(price ~ ln_sqft_living + grade + lat,
data = kc_houses)
summary(model3a)
Call:
lm(formula = price ~ ln_sqft_living + grade + lat, data = kc_houses)
Residuals:
Min 1Q Median 3Q Max
-1751991 -107963 -23688 66831 5297281
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -33416813 581524 -57.464 < 2e-16 ***
ln_sqft_living 276165 5462 50.557 < 2e-16 ***
grade3 -1997 261142 -0.008 0.9939
grade4 -116444 230028 -0.506 0.6127
grade5 -192182 226678 -0.848 0.3965
grade6 -218235 226302 -0.964 0.3349
grade7 -229124 226332 -1.012 0.3114
grade8 -170011 226403 -0.751 0.4527
grade9 -24016 226508 -0.106 0.9156
grade10 206343 226630 0.910 0.3626
grade11 564131 226890 2.486 0.0129 *
grade12 1201906 227935 5.273 1.35e-07 ***
grade13 2610142 235325 11.092 < 2e-16 ***
lat 673100 11207 60.060 < 2e-16 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 226100 on 21599 degrees of freedom
Multiple R-squared: 0.6209, Adjusted R-squared: 0.6206
F-statistic: 2721 on 13 and 21599 DF, p-value: < 2.2e-16autoplot(model3a)Warning: Removed 6866 row(s) containing missing values (geom_path).
Warning: Removed 1 rows containing missing values (geom_point).
Warning: Removed 1 row(s) containing missing values (geom_path).
###add interaction
coplot(resid ~ ln_sqft_living | lat,
panel = function(x, y, ...){
points(x, y)
abline(lm(y ~ x), col = "blue")
},
data = price_resid,
rows = 1)
latitude and ln_sqft_living not worth plotting
ln_sqft_living + grade + lat
price_resid %>%
ggplot(aes(x = lat, y = resid, colour = grade))+
geom_point(alpha = 0.1)+
geom_smooth(method = "lm", se = FALSE)`geom_smooth()` using formula 'y ~ x'
lat:grade has potential
price_resid %>%
ggplot(aes(x = ln_sqft_living, y = resid, colour = grade))+
geom_point(alpha = 0.1)+
geom_smooth(method = "lm", se = FALSE)`geom_smooth()` using formula 'y ~ x'
best one yet ln_sqft_living:grade
autoplot(model4a)
Warning: Removed 5717 row(s) containing missing values (geom_path).
Warning: Removed 1 rows containing missing values (geom_point).
Warning: Removed 3 row(s) containing missing values (geom_path).
model4b <- lm(price ~ ln_sqft_living + grade + lat +
lat:grade,
data = kc_houses)
summary(model4b)
Call:
lm(formula = price ~ ln_sqft_living + grade + lat + lat:grade,
data = kc_houses)
Residuals:
Min 1Q Median 3Q Max
-1614704 -104901 -25936 64782 5271323
Coefficients: (1 not defined because of singularities)
Estimate Std. Error t value Pr(>|t|)
(Intercept) -96315144 45502525 -2.117 0.0343 *
ln_sqft_living 275323 5434 50.672 <2e-16 ***
grade3 83723487 62949775 1.330 0.1835
grade4 71133733 49351547 1.441 0.1495
grade5 74000774 45842975 1.614 0.1065
grade6 72674921 45538076 1.596 0.1105
grade7 67029569 45509436 1.473 0.1408
grade8 60766368 45514094 1.335 0.1819
grade9 48478822 45533974 1.065 0.2870
grade10 36661297 45608326 0.804 0.4215
grade11 38151032 45927619 0.831 0.4062
grade12 -28417432 47641648 -0.596 0.5509
grade13 2475898 253927 9.750 <2e-16 ***
lat 1996518 957320 2.086 0.0370 *
grade3:lat -1763303 1327013 -1.329 0.1839
grade4:lat -1499152 1038414 -1.444 0.1488
grade5:lat -1561081 964486 -1.619 0.1056
grade6:lat -1533564 958062 -1.601 0.1095
grade7:lat -1414981 957459 -1.478 0.1395
grade8:lat -1282035 957556 -1.339 0.1806
grade9:lat -1020697 957974 -1.065 0.2867
grade10:lat -767634 959534 -0.800 0.4237
grade11:lat -791515 966230 -0.819 0.4127
grade12:lat 620491 1002196 0.619 0.5358
grade13:lat NA NA NA NA
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 224700 on 21589 degrees of freedom
Multiple R-squared: 0.6257, Adjusted R-squared: 0.6253
F-statistic: 1569 on 23 and 21589 DF, p-value: < 2.2e-16model4a best
anova(model3a, model4a)Analysis of Variance Table
Model 1: price ~ ln_sqft_living + grade + lat
Model 2: price ~ ln_sqft_living + grade + lat + ln_sqft_living:grade
Res.Df RSS Df Sum of Sq F Pr(>F)
1 21599 1.1044e+15
2 21589 9.9906e+14 10 1.0534e+14 227.64 < 2.2e-16 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1include as significant at all levels
###relative importance of variables
relaimpo::calc.relimp(model4a, type = "lmg", rela = TRUE)Response variable: price
Total response variance: 134782378397
Analysis based on 21613 observations
24 Regressors:
Some regressors combined in groups:
Group grade : grade3 grade4 grade5 grade6 grade7 grade8 grade9 grade10 grade11 grade12 grade13
Group ln_sqft_living:grade : ln_sqft_living:grade3 ln_sqft_living:grade4 ln_sqft_living:grade5 ln_sqft_living:grade6 ln_sqft_living:grade7 ln_sqft_living:grade8 ln_sqft_living:grade9 ln_sqft_living:grade10 ln_sqft_living:grade11 ln_sqft_living:grade12 ln_sqft_living:grade13
Relative importance of 4 (groups of) regressors assessed:
grade ln_sqft_living:grade ln_sqft_living lat
Proportion of variance explained by model: 65.7%
Metrics are normalized to sum to 100% (rela=TRUE).
Relative importance metrics:
lmg
grade 0.52139911
ln_sqft_living:grade 0.05523707
ln_sqft_living 0.31354730
lat 0.10981652
Average coefficients for different model sizes:
1group 2groups 3groups 4groups
ln_sqft_living 528647.45 386004.61 376366.12 499162.04
grade3 63666.67 35202.77 3604351.43 8833169.25
grade4 72381.04 -13814.95 1421737.47 2654959.35
grade5 106523.97 -30045.74 1126368.10 2310960.64
grade6 159919.64 -13319.69 973091.87 2163168.50
grade7 260590.26 36082.43 777437.86 1760536.51
grade8 400852.77 139070.53 407463.76 783882.11
grade9 631513.19 330866.68 -190030.89 -258079.71
grade10 929771.07 597898.60 -1518347.22 -3264507.63
grade11 1354841.73 992075.43 -3569200.65 -7892172.22
grade12 2049222.00 1660547.58 -6632106.80 -14390993.21
grade13 3567615.39 3128177.25 -18633828.30 -39350216.24
lat 813411.58 691928.88 673100.15 670852.62
ln_sqft_living:grade3 NaN NaN -1172612.47 -1408594.59
ln_sqft_living:grade4 NaN NaN -505355.69 -456944.89
ln_sqft_living:grade5 NaN NaN -423302.17 -404437.36
ln_sqft_living:grade6 NaN NaN -377388.11 -381812.00
ln_sqft_living:grade7 NaN NaN -317029.46 -321161.49
ln_sqft_living:grade8 NaN NaN -199757.80 -182409.53
ln_sqft_living:grade9 NaN NaN -11515.97 -34118.31
ln_sqft_living:grade10 NaN NaN 367695.79 358522.69
ln_sqft_living:grade11 NaN NaN 929266.41 939120.16
ln_sqft_living:grade12 NaN NaN 1764312.24 1742690.06
ln_sqft_living:grade13 NaN NaN 4717480.91 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